Subgroups — C₉⋊#13133343 #29505802

Order 15300.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₅⋊D₈₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#13133343	—	3	1	no	maximal
3	C₅²×C₉×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₉⋊#66775	—	5	6	no	maximal
5	C₃×C₅⋊D₈₅	D₃	1	1	yes	characteristic
6	#13133343	—	9	1	no	Hall
7	C₉×D₈₅	—	5	6	no	—
8	C₃×C₅²×C₁₇	Dic₃	1	1	yes	characteristic
9	C₃⋊#66775	—	15	6	no	—
10	C₉⋊#1043	—	17	1	no	maximal, Hall
11	C₅⋊D₈₅	D₉	1	1	yes	characteristic
12	C₅×C₉×C₁₇	AGL(1,𝔽₅)	1	6	yes	complemented
13	C₉⋊#595	—	25	1	no	Hall
14	C₃×D₈₅	—	5	6	no	—
15	C₉×C₅⋊D₅	—	17	1	no	—
16	C₅²×C₁₇	Dic₉	1	1	yes	characteristic, complemented, Hall
17	#66775	—	45	6	no	—
18	C₉×D₁₇	—	25	1	no	—
19	C₃⋊#1043	—	51	1	no	—
20	C₃×C₅×C₁₇	ΓL(1,𝔽₁₆)	1	6	yes	—
21	C₅²×C₉	#595	1	1	yes	characteristic, complemented, Hall
22	C₃⋊#595	—	75	1	no	—
23	C₉⋊AGL(1,𝔽₅)	—	85	6	no	—
24	D₈₅	—	5	6	no	—
25	C₉×C₁₇	#1043	1	1	yes	characteristic, complemented, Hall
26	C₃×C₅⋊D₅	—	17	1	no	—
27	C₃×D₁₇	—	25	1	no	—
28	#1043	—	153	1	no	Hall
29	C₉×D₅	—	85	6	no	—
30	C₅×C₁₇	C₉⋊AGL(1,𝔽₅)	1	6	yes	complemented
31	C₃×C₅²	C₃⋊#595	1	1	yes	characteristic
32	#595	—	225	1	no	Hall
33	ΓL(1,𝔽₁₆)	—	255	6	no	—
34	C₃×C₁₇	C₃⋊#1043	1	1	yes	characteristic
35	C₅⋊D₅	—	17	1	no	—
36	C₅×C₉	#66775	1	6	yes	complemented
37	Dic₉	—	425	1	no	Hall
38	D₁₇	—	25	1	no	—
39	C₃×D₅	—	85	6	no	—
40	C₅²	C₉⋊#595	1	1	yes	characteristic, complemented, Sylow
41	AGL(1,𝔽₅)	—	765	6	no	—
42	C₂×C₉	—	425	1	no	—
43	C₁₇	C₉⋊#1043	1	1	yes	characteristic, complemented, Sylow
44	C₃×C₅	C₃⋊#66775	1	6	yes	—
45	Dic₃	—	1275	1	no	—
46	D₅	—	85	6	no	—
47	C₉	#13133343	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃	—	425	1	no	—
49	C₅	C₉⋊#66775	1	6	yes	complemented
50	C₄	—	3825	1	no	Sylow
51	C₃	C₃⋊#13133343	1	1	yes	characteristic
52	C₂	—	425	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₅²×C₉×C₁₇	C₄
Frattini	C₃	C₃⋊#13133343
socle	C₃×C₅²×C₁₇	Dic₃
prime radical	C₃×C₅⋊D₈₅	D₃
cosocle	C₉×C₅⋊D₈₅	C₂
LCS	G ▷ C₅²×C₉×C₁₇
UCS	C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₅²×C₉×C₁₇	C₄	semidirect
12. C₅×C₉×C₁₇	AGL(1,𝔽₅)	semidirect
16. C₅²×C₁₇	Dic₉	semidirect
21. C₅²×C₉	#595	semidirect
25. C₉×C₁₇	#1043	semidirect
30. C₅×C₁₇	C₉⋊AGL(1,𝔽₅)	semidirect
36. C₅×C₉	#66775	semidirect
40. C₅²	C₉⋊#595	semidirect
43. C₁₇	C₉⋊#1043	semidirect
47. C₉	#13133343	semidirect
49. C₅	C₉⋊#66775	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₉×C₅⋊D₈₅	2
C₃⋊#13133343	3
C₉⋊#66775	5
C₉⋊#1043	17

Subgroups — C9⋊#13133343 #29505802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉⋊#13133343 #29505802